The graph below shows the graph of f (x), its derivative f ′(x), and its second derivative f ′′(x). Which of the following is the correct statement?

Question

Thank you so much in advance! :)

A graph is shown with three functions. Function A is a parabola with a minimum of about 0 comma negative 8 crossing the y axis around x equals negative 0.8 and around x equals 0.8. Function B is a quartic function with 2 minimums around x equals negative 1.5 and x equals 1.5 and one maximum at x equals 0. Function C is a cubic function increasing to a local maximum at about negative 0.8 comma 4.25 then decreasing through an inflection point at the origin and then increasing around 0.8 comma negative 4.25 to the right.

A is f ′, B is f, C is f ′′.

 A is f ′′, B is f, C is f ′. 

A is f ′, B is f ′′. C is f. 

A is f, B is f ′, C is f ′′.

Answer 1

The Hard Way:

1. Graph the functions the best you can
2. Try to find the algebraic equivalents
3. For instance A(x) = 12.5x² - 8
4. Take their derivatives and solve

The Easy Way:

A(x) = ax²+...

B(x) = bx⁴+...

C(x) = cx³+...

We know that d/dx axⁿ = anx^(n-1).

Since the derivative reduces the power by one, then

B = f

C = f'

A = f"

So the the answer must be:

A is f ′′, B is f, C is f ′